A review of evolutionary graph theory with applications to game theory

Biosystems ◽  
2012 ◽  
Vol 107 (2) ◽  
pp. 66-80 ◽  
Author(s):  
Paulo Shakarian ◽  
Patrick Roos ◽  
Anthony Johnson
Keyword(s):  
Game Theory ◽  
Graph Theory ◽  
Evolutionary Graph Theory

scholarly journals Construction of arbitrarily strong amplifiers of natural selection using evolutionary graph theory

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Andreas Pavlogiannis ◽  
Josef Tkadlec ◽  
Krishnendu Chatterjee ◽  
Martin A. Nowak
Keyword(s):  
Graph Theory ◽  
Natural Selection ◽  
Evolutionary Graph Theory

Discrete Mathematics And Historical Analysis: A Study Of Magellan

1995 ◽  
Vol 88 (2) ◽  
pp. 106-112
Author(s):  
Arnold E. Perham ◽  
Bernadette H. Perham
Keyword(s):  
Game Theory ◽  
Graph Theory ◽  
Historical Analysis ◽  
Discrete Mathematics ◽  
Historical Narratives ◽  
Political Movements ◽  
Modeling Tools

Historical narratives often involve the lives of kings and queens, periods of exploration, or political movements. In these narratives, identifying the strategic elements and analyzing their interrelationships are interesting problems. Topics in discrete mathematics used to model conflict, like graph theory and game theory, could be helpful modeling tools of history.

scholarly journals Martingales and fixation probabilities of evolutionary graphs

2014 ◽  
Vol 470 (2165) ◽  
pp. 20130730 ◽  
Author(s):  
T. Monk ◽  
P. Green ◽  
M. Paulin
Keyword(s):  
Graph Theory ◽  
Random Walk ◽  
Large Population ◽  
Initial Population ◽  
Weak Selection ◽  
Simplifying Assumptions ◽  
Population Sizes ◽  
Fixation Probabilities ◽  
Evolutionary Graph Theory ◽  
Complete Bipartite Graphs

Evolutionary graph theory is the study of birth–death processes that are constrained by population structure. A principal problem in evolutionary graph theory is to obtain the probability that some initial population of mutants will fixate on a graph, and to determine how that fixation probability depends on the structure of that graph. A fluctuating mutant population on a graph can be considered as a random walk. Martingales exploit symmetry in the steps of a random walk to yield exact analytical expressions for fixation probabilities. They do not require simplifying assumptions such as large population sizes or weak selection. In this paper, we show how martingales can be used to obtain fixation probabilities for symmetric evolutionary graphs. We obtain simpler expressions for the fixation probabilities of star graphs and complete bipartite graphs than have been previously reported and show that these graphs do not amplify selection for advantageous mutations under all conditions.

scholarly journals Fixation Probabilities of Evolutionary Graphs Based on the Positions of New Appearing Mutants

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Pei-ai Zhang
Keyword(s):  
Markov Chain ◽  
Graph Theory ◽  
Evolutionary Dynamics ◽  
Chain Process ◽  
Fixation Probability ◽  
Spatial Structures ◽  
Single Level ◽  
Fixation Probabilities ◽  
Evolutionary Graph Theory

Evolutionary graph theory is a nice measure to implement evolutionary dynamics on spatial structures of populations. To calculate the fixation probability is usually regarded as a Markov chain process, which is affected by the number of the individuals, the fitness of the mutant, the game strategy, and the structure of the population. However the position of the new mutant is important to its fixation probability. Here the position of the new mutant is laid emphasis on. The method is put forward to calculate the fixation probability of an evolutionary graph (EG) of single level. Then for a class of bilevel EGs, their fixation probabilities are calculated and some propositions are discussed. The conclusion is obtained showing that the bilevel EG is more stable than the corresponding one-rooted EG.

Evolutionary Graph Theory

2015 ◽  
pp. 75-91
Author(s):  
Paulo Shakarian ◽  
Abhinav Bhatnagar ◽  
Ashkan Aleali ◽  
Elham Shaabani ◽  
Ruocheng Guo
Keyword(s):  
Graph Theory ◽  
Evolutionary Graph Theory

scholarly journals Réflexion sur la prévision en relations internationales

2005 ◽  
Vol 11 (2) ◽  
pp. 211-222
Author(s):  
Philippe Braillard
Keyword(s):  
Social Sciences ◽  
Game Theory ◽  
Graph Theory ◽  
International Relations ◽  
Operations Research ◽  
Systems Analysis ◽  
Delphi Technique ◽  
The Social ◽  
Qualitative Evolution ◽  
Research Decision

In the study of international relations, as indeed in all of the social sciences, reflections about the future are becoming increasingly numerous. They indicate frequently moreover a desire for systemization through recourse to rigourous techniques and procedures: the Delphi technique, the construction of scenarios, Systems analysis, operations research, decision matrices, graph theory, game theory, etc. This leads us to conclude often that the forecasting approach in international relations is undergoing a major quantitative and qualitative evolution. We seek to show however in this analysis that, contrary to appearances, forecasting research in international relations is characterized above all today by great epistemological weakness and by a remarkable incoherence, and that it is not therefore, for the most part, equal to its pretensions. We will attempt to determine why this is the case and if this situation is likely to change. In doing so, we will seek to identify both the possibilities and the limits of forecasting in this field.

scholarly journals Environmental evolutionary graph theory

2014 ◽  
Vol 360 ◽  
pp. 117-128 ◽  
Author(s):  
Wes Maciejewski ◽  
Gregory J. Puleo
Keyword(s):  
Graph Theory ◽  
Evolutionary Graph Theory

scholarly journals The two-mutant problem: clonal interference in evolutionary graph theory

2010 ◽  
Vol 3 (4) ◽  
pp. 189-194 ◽  
Author(s):  
Chris Paley ◽  
Sergei Taraskin ◽  
Stephen Elliott
Keyword(s):  
Graph Theory ◽  
Clonal Interference ◽  
Evolutionary Graph Theory

scholarly journals BUILDING UP SCHEDULES IN MULTIPROJECT DESIGN MANAGEMENT SYSTEMS

2021 ◽  
Vol 2021 (3) ◽  
pp. 105-114
Author(s):  
Alexey Sergeyevich Dobrynin ◽  
Stanislav Matveevich Kulakov ◽  
Alexander Sergeyevich Koynov
Keyword(s):  
Game Theory ◽  
Graph Theory ◽  
Discrete Optimization ◽  
Systems Analysis ◽  
Practical Interest ◽  
Project Planning ◽  
Management Systems ◽  
Design Management ◽  
Mathematical Apparatus ◽  
New Generation

The article focuses on the problem of algorithmizing the process of building schedules in various spheres of human activity by using the modern mathematical apparatus, as well as achievements in the field of systems analysis, game theory, and graph theory. Nowadays, there have been analyzed and determined the boundaries of the effective application of many well-known heuristic and metaheuristic algorithms, which have shown good results in practice. However, despite the achievements in the discrete optimization, scheduling and network planning, the new problems of drawing up so-called coordinated schedules in the field of multi-project planning, which take into account the preferences (requests, wishes) of specific schedule executors, are still of practical interest. There have been considered the approaches and main stages of solving the problems of constructing coordinated schedules in multi-project planning, which is relevant for the development of new generation software and tools

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